Question about limits and inequalities

[AxiomOfChoice]

If you have

<br /> T &lt; M + \epsilon,<br />

where \epsilon &gt; 0 is arbitrary, does this imply

<br /> T \leq M?<br />

 

[VeeEight]

Yes.

 

[Office_Shredder]

Suppose it wasn't. Let epsilon be T-M (which is positive). What do you conclude?